JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer DIRECTION (Qs. 82): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following-
    Let \[x,\,\,\,y,\,\,\,z\] are three integers lying between \[1\] and \[9\] such that \[x\,51,\,\,\,y\,41\] and \[z\,31\] are three digit numbers.
    Statement-1: The value of the determinant\[\left| \begin{matrix}    5 & 4 & 3  \\    x\,51 & y\,41 & z\,31  \\    x & y & z  \\ \end{matrix} \right|is\,\,zero\].
    Statement-2: The value of a determinant is zero if the entries in any two rows (or columns) of the determinant are correspondingly proportional.

    A)  Statement-1 is false, Statement-2 is true.

    B)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

    C)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

    D)  Statement-1 is true, Statement-2 is false.

    Correct Answer: D

    Solution :

    \[\Delta =\left| \begin{matrix}    5 & 4 & 3  \\    x\,51 & y\,41 & z\,31  \\    x & y & z  \\ \end{matrix} \right|\]         \[=\left| \begin{matrix}    5 & 4 & 3  \\    100x+51 & 100y+41 & 100z+31  \\    x & y & z  \\ \end{matrix} \right|\] \[=\left| \begin{matrix}    5 & 4 & 3  \\    1 & 1 & 1  \\    x & y & z  \\ \end{matrix} \right|\]   \[[{{R}_{2}}\to {{R}_{2}}-100{{R}_{3}}-10{{R}_{1}}]\] which is zero provided\[x,\,\,y,\,\,z\]are in\[A.P.\]

adversite


You need to login to perform this action.
You will be redirected in 3 sec spinner

Free
Videos